A Guide to Working with Data Handling

Teaching Approach

When teaching data handling skills, it’s important to talk about the statistical process. The six

interconnected stages of the process are: posing a question, collecting data, organizing

data, summarizing data, representing data and interpreting (analyzing) data.

In each video lesson, we explain and demonstrate only one or two examples of each

concept or method that we use. We leave it to you to reinforce the learning with many

examples for learners to work on in class and for homework. You can use the activities given

in the task video. Full answers are also provided for every worked example in each lesson

and for every activity in the Task Answers. In addition there are online resources provided

where you can find more examples.

To get the full benefit of the lessons, your learners need to engage actively with the concepts

presented. So, when you preview the videos, think about how to introduce each lesson and

what follow up activities will be useful. Also watch out for places in the video where you can

pause to have a class discussion. We have used this pause icon to suggest some of these

places to you.

This is an important section and it can be fun and enjoyable. Data Handling is a section

where you as the teacher can incorporate many real life issues or topics from your learners’

local communities. It is also a section where you as the teacher can expose the learners to

statistics and how they play a prevalent role in the local communities, for example, the

percentage of learners who drink while underage, or the number of people in the community

voting for each political party. They can look at how it affects the everyday lives of the

learners and members of the community. As a teacher, you can use Data Handling as a tool

to educate your learners, and it could be especially effective if you could pair it up with their

subject Life Orientation.

We have included additional activities to supplement the learning in the videos and the skills

covered in the task video. Use these as class activities or as homework exercises.

Video Summaries

Some videos have a ‘PAUSE’ moment, at which point the teacher or learner can choose to

pause the video and try to answer the question posed or calculate the answer to the problem

under discussion. Once the video starts again, the answer to the question or the right

answer to the calculation is given.

Mindset suggests a number of ways to use the video lessons. These include:

Watch or show a lesson as an introduction to a lesson

Watch of show a lesson after a lesson, as a summary or as a way of adding in some

interesting real-life applications or practical aspects

Design a worksheet or set of questions about one video lesson. Then ask learners to

watch a video related to the lesson and to complete the worksheet or questions, either in

groups or individually

Worksheets and questions based on video lessons can be used as short assessments or

exercises

Ask learners to watch a particular video lesson for homework (in the school library or on

the website, depending on how the material is available) as preparation for the next days

lesson; if desired, learners can be given specific questions to answer in preparation for

the next day’s lesson

1. How to Collect Data

This lesson focuses on the different methods that can be used to collect data.

Advantages and disadvantages, usefulness and appropriateness of each method will be

discussed through the use of examples.

2. Developing Questions

Learners are introduced to how to develop suitable, reliable and unbiased questions that

can be used to collect data. The lesson also introduces the concept of sample and

population, as well as what constitutes a good questionnaire.

3. Organising Data

The focus of this first lesson lies in the organizing and sorting of the data. This is done

through the use of frequency tables and tallies, after the data has already been collected.

The use of intervals in frequency tables is explored.

4. Trends in Data

The focus of this lesson is working with summarizing data and finding averages, in order

for various conclusions concerning the data to be made. We will also be looking into the

effects that outliers might have on the mean, median, mode and range.

5. Types of Graphs

The focus of this lesson is on the different types of graphs one can use to represent data

and how each type of bar graph offers a different overall picture of the data.

6. Manipulating Graphs

In this lesson we will focus on the different graphs that have been drawn incorrectly or

that have been altered to misrepresent data.

Resource Material

Resource materials are a list of links available to teachers and learners to enhance their experience of

the subject matter. They are not necessarily CAPS aligned and need to be used with discretion.

1. How to Collect Data

http://prezi.com/vijvu05p40pl/weydon-school-maths-10y1/

A Prezi presentation on different types of sampling.

http://www.mindset.co.za/resources//0000062933/0000136510/0000139974/LN%20Calculating%20with%20Data_L1.pdf

A Mindset worksheet on collecting data, aligned to NCS Mathematics.

http://www.mindset.co.za/resources//0000062935/0000136512/0000139976/LN%20Calculating%20with%20Data_L2.pdf

A Mindset note on how to collect data, aligned to NCS Mathematics.

2. Developing Questions

http://www.flickr.com/photos/83006968@N06/7635447286/

Examples of types of questionnaires and types of questions. http://www.flickr.com/photos/4719482

3@N02/4327782900/

http://www.bbc.co.uk/schools/gcsebitesize/dida/managing_projects/evaluatingrev6.shtml

3. Organising Data

http://www.bbc.co.uk/schools/gcsebitesize/maths/statistics/representingdata3hirev1.shtml

Classifying data into different types.

http://www.flickr.com/photos/61891052@N02/5678591925/

Organising Data using a tally table.

4. Trends in Data

http://www.bbc.co.uk/schools/gcsebitesize/maths/statistics/measuresofaveragerev3.shtml

Understanding the measures of central tendencies (mean, median and mode).

http://www.bbc.co.uk/schools/gcsebitesize/maths/statistics/measuresofaveragerev6.shtml

Advantages and disadvantages of mean, median and mode.

5. Types of Graphs

http://www.basic-mathematics.com/bar-graphs.html

Understanding bar graphs

http://www.basic-mathematics.com/bar-graphs.html

http://www.emathzone.com/tutorials/basic-statistics/component-bar-chart.html

Understanding compound bar graphs.

http://www.mathsisfun.com/data/pie-charts.html

Understanding how to draw a pie chart.

http://www.edplace.com/worksheet_preview.php?eId=1975&type=nc

How to read and understand a pie chart.

http://www.mathgoodies.com/lessons/graphs/line_graph_part2.html

Understanding line graphs.

http://www.bbc.co.uk/bitesize/ks3/maths/handling_data/representing_data/revision/3/

Broken line graphs and trends.

6. Manipulating Graphs

http://www.youtube.com/watch?v=oGGYIw_pIj8&feature=related

A YouTube clip with multiple statistics which will provide for interesting debate in class.

http://en.wikipedia.org/wiki/Sampling_bias

Sampling bias: This offers advanced enrichment for a teacher and not recommended for learners.

http://www.mathsisfun.com/data/survey-conducting.html

How to do a survey: Site also has interactive games and printable worksheets for all junior grades.

Task

Question 1

Look at the following questions and state if they are reliable or not. If not, rewrite the

question to make it reliable.

1.1 Do you own a laptop?

1.2 If you do have a laptop, do you use it for schoolwork?

1.3 Do you drink alcohol?

1.4 Have you ever drunk alcohol while underage at school?

1.5 How old are you?

1.6 What age should it be made legal for learners to smoke at school?

1.7 Do you play a sport at school or with a club?

Question 2

For each of the following scenarios, decide which method of collecting data would be the

best choice. Provide a reason for your answer.

2.1 Gathering data about the choice of sports learners in Grade 10 do at your local school.

2.2 Gathering data about the vehicles that drive past the spaza shop between the times of

14:00 and 17:00 every Monday, Wednesday and Friday.

2.3 Gathering data about why learners do not like attending assembly at school.

Question 3

3.1 Data can be classified into two main types. What are these two types?

3.2 What is the difference(s) between discrete and continuous data?

3.3 Classify each of the following statements below as categorical, discrete or continuous

data.

3.3.1 The number of SMSs you send per day.

3.3.2 The number of Grade 11’s who play soccer at your school.

3.3.3 The temperature in Pretoria over the months of June and July.

3.3.4 The brands of cellphones that the learners in your school own.

Question 4

The Grade 11’s with their Life Science teacher conducted a study using fifty bean plants.

These plants were measured in centimetres to see how tall they were. The heights were

rounded to the nearest centimetre. After each plant was measured, the data was recorded

in groups and a frequency table was constructed. The frequency table is shown below.

Study the frequency table and answer the following questions.

4.1 Complete the following table by adding in the tally.

Height of bean

plants (cm) Tally

Number of

plants

20 - 24 2

25 - 29 6

30 - 34 14

35 - 39 16

40 - 44 10

45 - 49 2

Total 50

4.2 How many bean plants had the height of less than 35cm?

4.3 How many bean plants had the height of 19cm or less?

4.4 How many bean plants had the height of between 25 – 44cm?

4.5 What conclusions could you draw from this frequency table and the data?

Question 5

Your school principal is very interested in what types of food the learners are buying at the

school tuck shop. He believes that a healthier approach to school lunches is needed.

Here is a pie chart that shows the type of lunches bought by a random sample of 50

learners.

Use the pie chart to answer the following questions.

5.1 How many learners completed the survey?

5.2 How many of the learners bought pies?

5.3 Estimate what fraction of learners bought burgers.

5.4 Estimate what fraction of learners bought hotdogs.

5.5 What was the most and least popular choice of tuck shop food?

5.6 How many degrees is represented by each sector of the pie chart?

Burger 24%

Pie 28%

Hotdog 48%

TUCKSHOP MEALS SOLD

Question 6

The data set below shows the number of hours in a week twenty-five teenagers spent

watching television. Their times have been rounded off and are correct to the nearest hour.

17 14 18 19 12

6 15 13 12 10

11 16 10 15 30

22 7 12 24 5

25 8 9 16 27

6.1 Arrange the data in ascending order.

6.2 Calculate the mean (average) time teenagers spent watching television. Round your

answer off to the nearest hour.

6.3 What does the mean tell us about the time teenagers spent watching television?

6.4 Calculate the median.

6.5 Why should we use the mean to discuss this data, instead of the median or mode?

Question 7

Study the following graph, and answer the following questions.

7.1 What are your first impressions of seeing this graph? Describe what do you see the

graph is portraying, as if you were explaining this to your parents.

7.2 Do you think that the graph is misleading? If yes, in what ways is this graph misleading?

Task Answers

Question 1

1.1 Reliable

1.2 Unreliable – not all learners would have a laptop, and could have answered “no” to the previous

question. Rather ask, “do you use a computer to help you with your school work?”

1.3 This question could be reliable, as it is straight forward, however, one needs to know the context

behind this question.

1.4 Unreliable – the question is judgemental and learners could lie in their answers. Rather ask,

“Have you ever drunk alcohol?”

1.5 Reliable

1.6 It is a reliable question, but whether it is an appropriate question to ask school learners or not is

the issue. Choice answers might need to be provided.

1.7 Reliable

Question 2

2.1 Questionnaire. It is an excellent way of collecting data concerning a specific point from large

amounts of people. It is quick and easy to do.

2.2 Observation. In this scenario, you would be collecting data about either the colour or make of the

cars. It would not be possible (or safe) to ask the drivers of the cars for this information. By

observing, you are able to collect this data from a safe distance.

2.3 Interviews. By speaking face to face with the learners, you would be able to collect accurate,

personal information. The learners should give a variety of responses instead of just choosing a

readymade multiple - choice answer.

Question 3

3.1 Categorical and numerical data.

3.2 Discrete data usually contain certain whole individual numbers and no values in between, where

continuous data can contain fractions and can be any value.

3.3.1 Discrete

3.3.2 Discrete

3.3.3 Continuous

3.3.4 Categorical

Question 4

4.1

4.2 14 + 6 + 2 = 22

4.3 0

4.4 6 + 14 + 16 + 10 = 46

4.5 One can see that the majority of the bean plants grew to a height of between 35-39cm. The least

amount of plants grew to heights of between 20-24cm and 45-49cm.

Question 5

5.1 50 learners

5.2

learners

5.3

5.4

5.5 Most popular: hot dogs. Least popular: Burgers

5.6 Pies:

Burgers:

Hotdogs:

Therefore,

Question 6

6.1

6.2

6.3 The mean tells us the average amount of time the all 25 teenagers spent watching TV in one

week, and approximately 14 hours is a lot of time spent watching TV.

6.4 Median = 14.

6.5 We should use the mean instead of the median and mode because the mean uses all of the

data, and does not leave out data like the median and mode.

Question 7

7.1 This graph could be used by a learner to indicate how his or her Math’s marks are improving over

the term.

7.2 Yes, it is misleading. There are two problems with the vertical axis: the first is that the highest

mark on the axis is 50%, which could draw our attention away from the fact that the learner’s

marks are so poor. The axis should extend to 100%, because that is the highest mark achievable

for each test. The second is that the scale of the axis has been enlarged, so it exaggerates the

increase in the percentages. In reality, the marks range from 46% to 50%, which is not a big

change in this context.

Additional Activities

Activity 1

The schools in your local district conducted survey with certain learners about which mode of

transport learners used to get to school, and back home again. The survey consisted of five

questions. One of the questions was: “What mode of transport do you use to get to and from school?”

Here are the responses:

walk bicycle taxi walk car

bicycle bicycle walk walk car

Walk bus walk taxi walk

car bus bus bus bus

car walk bus skateboard taxi

taxi motorcycle bus motorcycle skateboard

walk bicycle walk bus car

walk taxi bicycle walk bus

1.1 How many people took part in the survey?

1.2 Construct a frequency table that represents this data.

1.3 What mode of transport was the least used? Give a reason for your answer as to why do you

think so.

1.4 What conclusions could you draw from this frequency table and the data?

Activity 2

A Grade 11 learner has conducted a survey to determine which colour of car was the most popular.

As her time was limited, she conducted the survey on the first 200 cars that passed a certain point on

the main road. She calculated the following data:

Colour Percentage of

vehicles

Number of

vehicles

The angle of

segment

Red 11

Green 3

White 44

Blue 14

Silver 11

Other 17

Use the above table and information to answer the following questions. Remember to show all of your

working out.

2.1 Calculate the number of vehicles there were per colour.

2.2 Calculate the number degrees per car colour segment.

2.3 Using the table, construct an accurate pie chart. Measure each angle to see if the pie chart was

drawn accurately.

2.4 How would you know if your pie chart was accurately drawn?

Activity 3:

Two schools were invited to compete against each other in a Mathematics competition. School A was

from the Western Cape and School B was from Gauteng. Each school has six Grade 11 classes. The

table below shows the mean averages of each class, per school, after taking part in the competition.

School A 27 33 33 45 47 51

School B 25 29 37 42 42 51

3.1 Find the measures of central tendencies for both school A and B. Show all calculations.

3.2 Calculate the range (measure of dispersion) for each school. Show all calculations.

3.3 Is range a good tool to compare the two schools? Explain your answer.

Additional Activities Answers

Activity 1

walk bicycle taxi walk car

bicycle bicycle walk walk car

Walk bus walk taxi walk

car bus bus bus bus

car walk bus skateboard taxi

taxi motorcycle bus motorcycle skateboard

walk bicycle walk bus car

walk taxi bicycle walk bus

1.1 40 people

1.2

Mode of Transport Frequency

Walking 12

Bus 9

Taxi 5

Motorcycle 2

Car 5

Skateboard 2

Bicycle 5

TOTAL 40

1.3 There are two modes – motorcycle and skateboard. Possible reasons for this could be that a

motorcycle is expensive to buy and run.

1.4 The most popular form of transport to and from school is walking, closely followed by taking the

bus. However, the least popular is using a motorcycle or a skateboard.

Activity 2

Colour Percentage of

vehicles

Number of

vehicles

The angle of

segment

Red 11 22 40

Green 3 6 11

White 44 88 158

Blue 14 28 50

Silver 11 22 40

Other 17 34 61

2.1 See table

2.2 See table

2.3 2.4 All of the angles would add up to 360 degrees.

Activity 3

Two schools were invited to compete against each other in a Mathematics competition. School A was

from the Western Cape and School B was from Gauteng. Each school has six Grade 11 classes. The

table below shows the mean averages of each class, per school, after taking part in the competition.

School A 27 33 33 45 47 51

School B 25 29 37 42 42 51

3.1 School A:

Mean =

Median = ;

Mode = 33

School B:

Mean =

Median = ;

Mode = 42

3.2 School A =

School B =

3.3 No, it is not. The range only tells us how spread out or close together the data is. It does not tell

us any useful information like the measures of central tendencies.

Acknowledgements

Mindset Learn Executive Head Dylan Busa

Content Manager Classroom Resources Jenny Lamont

Content Coordinator Classroom Resources Helen Robertson

Content Administrator Agness Munthali

Content Developer Meryl Diab

Content Reviewer Bernard Donkor

Produced for Mindset Learn by Traffic

Facilities Coordinator Cezanne Scheepers

Production Manager Belinda Renney

Director: Alriette Gibbs

Editor: Nonhlanhla Nxumalo

Presenter: Talitha Ndima

Studio Crew: Abram Tjale

James Tselapedi

Wilson Mthembu

Graphics: Wayne Sanderson.

This resource is licensed under a Attribution-Share Alike 2.5 South Africa licence. When using this

resource please attribute Mindset as indicated athttp://www.mindset.co.za/creativecommons